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Proof step 15 from proof junkrefs-put-nopathex-equiv (previous step)

st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_valid_ref(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r2 ' + refs, ty1, st), path∃(str, r2, r0, st), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, path∃(str, r1, r0, st), junkrefs(str, r2 ' + refs, ty1, st[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_obj(str, r, st) ∧ r ≠ r0 → ( path∃(str, r, r0, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ ( st[r -- fs '] .refval ≠ jvmref ∧ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r -- fs '] .refval, r0, st) ∨ st[r -- fs '] .refval = jvmref ∧ r0 = jvmref)))
Proof step 14:
is_obj(str, r1, st) ∧ r1 ≠ r0, st[r1 -- mkfs(class, ty1, fieldvar) '] = refval(r2), st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_valid_ref(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r2 ' + refs, ty1, st), path∃(str, r2, r0, st), ∀ str0, r, st0, sk0, ty0, val0. ¬ path∃(str0, r2, r, st0) ∧ is_valid_ref(str0, r, st0) ∧ sk0 ≠ _type → (junkrefs(str0, r2 ' + refs, ty0, st0[r -- sk0, val0]) ↔ junkrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = r1, r1 = jvmref, sk = _type, ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ ( st[r1 -- fs '] .refval ≠ jvmref ∧ st[st[r1 -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r1 -- fs '] .refval, r0, st) ∨ st[r1 -- fs '] .refval = jvmref ∧ r0 = jvmref), junkrefs(str, r2 ' + refs, ty1, st[r0 -- sk, val])

Rule argument

[crewrite-arg: pathex-class, F, [st, r0, r, str] → [st, r0, r1, str]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, r0, r1, str)]]